CALL: FIT_POLYA
The histogram is referenced via a global variable that has usually
been returned by a call to BOOK_HISTOGRAM or GET_HISTOGRAM. This
argument may also be an expression that results in a histogram.
The argument is not modified on return.
A 1-dimensional array that contains the ordinates of the
points to be fitted.
The vectors x, y and err_y must have the same length,
unless err_y is given as a scalar.
Not changed on exit.
A 1-dimensional array that contains the coordinates of the
points to be fitted.
The vectors x, y and err_y must have the same length,
unless err_y is given as a scalar.
In the initial estimate, the data points where y <= 0 are
skipped. If there are many such points which should
be taken into account for the fit, then convergence is
not guaranteed.
Not changed on exit.
A 1-dimensional array that contains the errors on the
coordinates of the points to be fitted.
This argument can also be a scalar, which is then used as
error for all points. If this argument is a vector, then
it must have the same length as x and y.
Not changed on exit.
The function that is fitted to the data points is given by
function = factor*slope *
((theta+1)**(theta+1)/Gamma(theta+1) *
(offset+slope*X)**theta *
exp(-(theta+1)*(offset+slope*X))
i.e. a Polya distribution with argument offset+slope*X and
with Polya parameter theta.
The input values for the terms are used as initial values for
the fit if the MANUAL option is used (this is not default).
The parameters "offset" and "slope" are fitted if the option
FIT is specified, otherwise the values have to be specified on
input.
Parameters of which the value on input is to be used, must be
of type Number.
All arguments except "offset" and "slope" when using the FIX
option, must be modifiable, i.e. it can not be a constant nor
an expression.
The errors returned are the square roots of the diagonal elements
of the covariance matrix, multiplied by a correction factor equal
to:
sqrt(chi**2/(#points - #parameters))
This correction factor is equal to 1 if the errors to the data
points have been assigned correctly.
These arguments must be modifiable, that is, they can neither be
constants nor expressions.
The options string may contain the keywords listed in the table
below. The keywords should be separated by blanks or commas.
Additional text may be added - no error message will be issued
if unrecognised keywords are used.
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Option Meaning Defaults
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AUTO Determine suitable starting values Default
EQUAL Assume equal weight of all points Not default
FIT Fit the scale of the distribution Default
FIX Don't modify the scale parameters Not default
MANUAL Start from given initial values Not default
NOPLOT Don't plot the histogram and fit Default
NOPRINT Don't print details during the fit Default
PLOT Plot the histogram with fit Not default
POISSON Assume Poisson errors Default
PRINT Print details during the fit Not default
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Note: The EQUAL and POISSON options are ignored for matrix fits since
the errors on the points are explicitely provided in that case.
The plot is always made on a linear-logaritmic scale.
Keyword index.
Formatted on 10/11/98.